Question: What is the greatest divisor of 372 that is smaller than 50 and also a factor of 72?
Answer: We can list all of the positive factors of 372.  They are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, and 372.  The greatest of these that is less than 50 is 31.  However, 31 is not also a factor of 72.  The positive factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.  Then, we can see that the greatest divisor of 372 less than 50 that is also a factor of 72 is $\boxed{12}$.